package euler.p101_150;

import euler.MainEuler;

public class Euler108 extends MainEuler {

    /*
        In the following equation x, y, and n are positive integers.
        1/x + 1/y = 1/n

        For n = 4 there are exactly three distinct solutions:
            1/5 + 1/20 = 1/4
            1/6 + 1/12 = 1/4
            1/8 + 1/8 = 1/4

        What is the least value of n for which the number
        of distinct solutions exceeds one-thousand?

        NOTE: This problem is an easier version of problem 110;
        it is strongly advised that you solve this one first.

     */
    public String resolve(int limite) {

        int soluciones = 0;
        for (int n = 5; soluciones <= limite; n++) {
            soluciones = (primeHelper.divisores((long)n*n).size() + 1)/ 2;

            if (soluciones > limite) {
            	return String.valueOf(n);
                // 180180
            }
        }

        return null;
    }

}
